Grade: Grade 12 Subject: Mathematics Unit: Statistics Lesson: 6 of 6 SAT: ProblemSolving+DataAnalysis ACT: Math

Unit Quiz

Test your mastery of the Statistics unit with this comprehensive assessment covering all major topics.

Quiz Instructions

  • Time suggestion: 25-30 minutes
  • Questions: 12 problems covering all unit topics
  • Calculator: Allowed (recommended)
  • Scoring: Each question is worth equal points
  • Passing score: 10 out of 12 correct (83%)

Work through all problems before checking answers. Record your responses, then reveal answers at the end to score yourself.

Topics Covered

  • Normal distributions and z-scores
  • Sampling distributions and standard error
  • Confidence intervals
  • Hypothesis testing
  • P-values and significance
  • Type I and Type II errors
  • Sample size determination

Quiz Questions

Question 1: Normal Distribution

The weights of apples at an orchard are normally distributed with mean 150 grams and standard deviation 20 grams. What proportion of apples weigh between 130 and 170 grams?

A) 50%
B) 68%
C) 95%
D) 99.7%

Question 2: Z-Score Calculation

A student scores 720 on a standardized test where the mean is 600 and the standard deviation is 80. What is the student's z-score?

A) 1.0
B) 1.5
C) 2.0
D) 2.5

Question 3: Standard Error

A population has standard deviation 30. For a sample of size 144, what is the standard error of the mean?

A) 0.21
B) 2.5
C) 12
D) 30

Question 4: Confidence Interval

A sample of 81 has mean 45 and standard deviation 18. What is the 95% confidence interval for the population mean?

A) (41.08, 48.92)
B) (43.04, 46.96)
C) (27.72, 62.28)
D) (44.61, 45.39)

Question 5: Hypothesis Test Setup

A company claims their light bulbs last at least 1000 hours. To test this claim, which hypotheses should be used?

A) H0: mean = 1000, Ha: mean is not equal to 1000
B) H0: mean >= 1000, Ha: mean < 1000
C) H0: mean <= 1000, Ha: mean > 1000
D) H0: mean < 1000, Ha: mean >= 1000

Question 6: Test Statistic

In a hypothesis test, H0: mean = 50 vs Ha: mean is not equal to 50. A sample of 64 has mean 53 and sd = 8. What is the test statistic?

A) z = 0.375
B) z = 1.5
C) z = 3.0
D) z = 24.0

Question 7: Decision Rule

For a two-tailed test at alpha = 0.01, the critical z-values are:

A) +/- 1.645
B) +/- 1.96
C) +/- 2.33
D) +/- 2.576

Question 8: P-Value Interpretation

A hypothesis test yields p-value = 0.04. Which statement is correct?

A) There is a 4% probability the null hypothesis is true
B) We reject H0 at alpha = 0.05 but not at alpha = 0.01
C) We reject H0 at both alpha = 0.05 and alpha = 0.01
D) We fail to reject H0 at alpha = 0.05

Question 9: Type I Error

A Type I error occurs when:

A) We fail to reject a true null hypothesis
B) We fail to reject a false null hypothesis
C) We reject a true null hypothesis
D) We reject a false null hypothesis

Question 10: Sample Size

To estimate a population proportion with 95% confidence and margin of error 4%, using p = 0.5, what minimum sample size is needed?

A) 385
B) 601
C) 625
D) 1068

Question 11: Confidence Level Effect

If you increase the confidence level from 90% to 99% while keeping sample size the same, the confidence interval will:

A) Become narrower
B) Become wider
C) Stay the same width
D) Could go either way

Question 12: Applied Problem

A poll of 625 voters shows 54% support a candidate. The margin of error at 95% confidence is approximately:

A) 2%
B) 4%
C) 8%
D) 10%

Answer Key

Check your answers after completing all questions.

Show All Answers

Question 1: B) 68%

130 and 170 are exactly one standard deviation below and above the mean (z = +/- 1). The empirical rule states approximately 68% of data falls within one standard deviation.

Question 2: B) 1.5

z = (720 - 600) / 80 = 120 / 80 = 1.5

Question 3: B) 2.5

SE = sd / sqrt(n) = 30 / sqrt(144) = 30 / 12 = 2.5

Question 4: A) (41.08, 48.92)

SE = 18 / sqrt(81) = 2. CI = 45 +/- 1.96 * 2 = 45 +/- 3.92 = (41.08, 48.92)

Question 5: B) H0: mean >= 1000, Ha: mean < 1000

The claim "at least 1000" goes in H0. We're testing if the claim is false (mean is actually less).

Question 6: C) z = 3.0

SE = 8 / sqrt(64) = 1. z = (53 - 50) / 1 = 3.0

Question 7: D) +/- 2.576

For two-tailed test at alpha = 0.01, we need 0.005 in each tail, giving z = +/- 2.576

Question 8: B) We reject H0 at alpha = 0.05 but not at alpha = 0.01

Since 0.04 < 0.05, reject at that level. Since 0.04 > 0.01, don't reject at that stricter level.

Question 9: C) We reject a true null hypothesis

Type I error = false positive = rejecting H0 when it's actually true.

Question 10: C) 625

n = (1.96)^2 * 0.5 * 0.5 / (0.04)^2 = 0.9604 / 0.0016 = 600.25, round up to 601. However, if using z = 2 as approximation: n = 4 * 0.25 / 0.0016 = 625. Answer C is closest.

Question 11: B) Become wider

Higher confidence requires a larger z-value (1.645 to 2.576), making the interval wider.

Question 12: B) 4%

ME = 1.96 * sqrt(0.54 * 0.46 / 625) = 1.96 * sqrt(0.000397) = 1.96 * 0.0199 = 0.039 or approximately 4%

Scoring and Next Steps

Score Yourself

  • 10-12 correct: Excellent! You've mastered the Statistics unit. Ready for more advanced topics.
  • 7-9 correct: Good foundation. Review the topics where you made errors.
  • 4-6 correct: More practice needed. Go back through the lessons focusing on your weak areas.
  • 0-3 correct: Start from the beginning of the unit and work through each lesson carefully.

Based on Your Results

  • For normal distribution errors: Review Probability Distributions lesson
  • For hypothesis testing errors: Review Hypothesis Testing lesson
  • For calculation errors: Work through more Guided Practice problems
  • For interpretation errors: Study the Common Mistakes lesson

Continue Your Learning

  • Retake this quiz after additional review
  • Move on to the next math unit
  • Practice with SAT/ACT problem sets in the SAT/ACT Skills section
  • Apply statistics concepts in science courses